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How do you evaluate the limit #x/(sqrt(3x^2+1)# as x approaches #oo#?

Answer 1

Emma Aldridge

#1/sqrt3#

Let #L = lim_(x->oo) x/(sqrt(3x^2+1))#

#= lim_(x->oo) (x/x)/(1/x(sqrt(3x^2+1)))#

#= lim_(x->oo) 1/sqrt((1/x^2(3x^2+1)))#

#= lim_(x->oo) 1/sqrt((3 + 1/x^2))#

#= 1/(sqrt(3+0)) = 1/sqrt3#

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Answer 2

Christopher Agresta

To evaluate the limit of x/(sqrt(3x^2+1)) as x approaches infinity, we can use the concept of limits. By dividing both the numerator and denominator by x, we can simplify the expression. This results in 1/(sqrt(3+(1/x^2))). As x approaches infinity, 1/x^2 approaches zero. Therefore, the expression simplifies to 1/(sqrt(3+0)), which is equal to 1/sqrt(3). Hence, the limit of x/(sqrt(3x^2+1)) as x approaches infinity is 1/sqrt(3).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.